To solve the quadratic equation \(2x^2 + 3x + 1 = 0\), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here, the coefficients are \(a = 2\), \(b = 3\), and \(c = 1\).

1. Calculate the discriminant \(\Delta\):

\[ \Delta = b^2 - 4ac = 3^2 - 4 \cdot 2 \cdot 1 = 9 - 8 = 1 \]

2. Substitute the values into the quadratic formula:

\[ x = \frac{-3 \pm \sqrt{1}}{2 \cdot 2} = \frac{-3 \pm 1}{4} \]

3. Solve for the two possible values of \(x\):

\[ x_1 = \frac{-3 + 1}{4} = \frac{-2}{4} = -\frac{1}{2} \]
\[ x_2 = \frac{-3 - 1}{4} = \frac{-4}{4} = -1 \]

Therefore, the solutions to the equation \(2x^2 + 3x + 1 = 0\) are:

\[ x = -\frac{1}{2} \text{ and } x = -1 \]

Would you like more details or have any questions?

Here are 5 more questions you can ask:
1. How do you complete the square for a quadratic equation?
2. What is the quadratic formula used for solving equations?
3. How do you factorize quadratic equations?
4. Can you solve the equation \(x^2 - 4x + 4 = 0\)?
5. What are the applications of solving quadratic equations in real life?

Tip: When solving quadratic equations, always check the discriminant (\(\Delta = b^2 - 4ac\)) first to determine the nature of the roots (real and distinct, real and equal, or complex).

Learn how to solve the quadratic equation 2x^2 + 3x + 1 = 0 with a detailed step-by-step solution using the quadratic formula. Understand the discriminant and its role in determining the nature of roots. Suitable for high school students in Grades 10-12.

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